Pseudo-Riemannian manifolds with recurrent spinor fields

详细信息    查看全文

• 作者：A. S. Galaev (1)
  
• 关键词：pseudo ; Riemannian manifold ; recurrent spinor field ; holonomy algebra
• 刊名：Siberian Mathematical Journal
• 出版年：2013
• 出版时间：July 2013
• 年：2013
• 卷：54
• 期：4
• 页码：604-613
• 全文大小：196KB
• 参考文献：1. / Hitchin N., 鈥淗armonic spinors,鈥?Adv. Math., 14, 1鈥?5 (1974). CrossRef
  2. / Friedrich Th., 鈥淶ur Existenz paralleler Spinorfelder 眉ber Riemannschen Mannigfaltigkeiten,鈥?Colloq. Math., 44, No. 2, 277鈥?90 (1981).
  3. / Wang M., 鈥淧arallel spinors and parallel forms,鈥?Ann. Global Anal. Geom., 7, No. 1, 59鈥?8 (1989). CrossRef
  4. / Leistner Th., 鈥淟orentzian manifolds with special holonomy and parallel spinors,鈥?Rend. Circ. Mat. Palermo (2) Suppl., No. 69, 131鈥?59 (2002).
  5. / Leistner Th., Holonomy and Parallel Spinors in Lorentzian Geometry, Logos-Verlag and Humboldt-Universit盲t zu Berlin, Berlin (2003).
  6. / Baum H. and Kath I., 鈥淧arallel spinors and holonomy groups on pseudo-Riemannian spin manifolds,鈥?Ann. Global Anal. Geom., 17, No. 1, 1鈥?7 (1999). CrossRef
  7. / Ikemakhen A., 鈥淕roupes d鈥檋olonomie et spineurs parall猫les sur les vari茅t茅s pseudo-riemanniennes compl猫tement r茅ductibles,鈥?C. R. Math. Acad. Sci. Paris, 339, No. 3, 203鈥?08 (2004). CrossRef
  8. / Moroianu A., 鈥淧arallel and Killing spinors on Spinc manifolds,鈥?Comm. Math. Phys., 187, No. 2, 417鈥?27 (1997). CrossRef
  9. / Ikemakhen A., 鈥淧arallel spinors on pseudo-Riemannian Spin^c manifolds,鈥?J. Geom. Phys., 56, No. 9, 1473鈥?483 (2006). CrossRef
  10. / Ikemakhen A., 鈥淧arallel spinors on Lorentzian Spin^c manifolds,鈥?Differential Geom. Appl., 25, No. 3, 299鈥?08 (2007). CrossRef
  11. / Galaev A. S., 鈥淢etrics that realize all Lorentzian holonomy algebras,鈥?Int. J. Geom. Methods Mod. Phys., 3, No. 5鈥?, 1025鈥?045 (2006). CrossRef
  12. / Galaev A. S. and Leistner Th., 鈥淗olonomy groups of Lorentzian manifolds: classification, examples, and applications,鈥?in: Recent Developments in Pseudo-Riemannian Geometry, Eur. Math. Soc., Z眉rich, 2008, pp. 53鈥?6 (ESI Lect. Math. Phys.). CrossRef
  13. / Berard Bergery L. and Ikemakhen A., 鈥淥n the holonomy of Lorentzian manifolds,鈥?Proc. Sympos. Pure Math., 54, 27鈥?0 (1993). CrossRef
  14. / Leistner T., 鈥淥n the classification of Lorentzian holonomy groups,鈥?J. Differential Geom., 76, No. 3, 423鈥?84 (2007).
  15. / Armstrong S., 鈥淩icci-flat holonomy: a classification,鈥?J. Geom. Phys., 57, No. 6, 1457鈥?475 (2007). CrossRef
  
• 作者单位：A. S. Galaev (1)
  
  1. University of Hradec Kr谩lov茅, Hradec Kr谩lov茅, Czech Republic
  
• ISSN：1573-9260

文摘

The existence of a recurrent spinor field on a pseudo-Riemannian spin manifold (M,g) is closely related to the existence of a parallel 1-dimensional complex subbundle of the spinor bundle of (M,g). We characterize the following simply connected pseudo-Riemannian manifolds that admit these subbundles in terms of their holonomy algebras: Riemannian manifolds, Lorentzian manifolds, pseudo-Riemannian manifolds with irreducible holonomy algebras, and pseudo-Riemannian manifolds of neutral signature admitting two complementary parallel isotropic distributions.